Mar. 20th, 2007

sniffnoy: (SMPTE)
Munkres's Topology, Section 45, exercise 8; we have metric spaces X and Y, the product space X×Y under the max metric; and H, the space of all nonempty, closed, bounded subsets of X×Y under the Hausdorff metric. So Munkres tells us to consider the function gr:C(X,Y)→H (where C(X,Y) is considered in the uniform metric, for the record), where gr assigns to each function its graph, and then...

...well, "and then" doesn't actually matter for now, because gr isn't actually a function from C(X,Y) to H unless we impose some more conditions. For f∈C(X,Y), gr(f) is always closed, but is bounded iff X and f(X) are. So we'll have to require X bounded, but that's not nearly enough to force all continuous functions from X to Y to be bounded... we could limit ourselves to X compact, but that's clearly not what Munkres intended as part (c) of the problem requires a continuous f:X→Y that's not uniformly continuous. We could limit ourselves to Y bounded, but I suspect that if that were the intention, the book would just say "nonempty closed subsets" rather than "nonempty closed bounded subsets". Maybe it's supposed to be BC(X,Y)? Maybe we're just supposed to assume every f∈C(X,Y) is bounded? Maybe there was supposed to be some additional condition which would ensure this? Maybe we were supposed to take the standard bounded metrics on X,Y obtained from dX, dY? Or just on the product space? [And of course in addition to all this we have to assume X bounded if that's not already implied.]

Looking up the errata for Munkres, there are no errata for this page (page 281) (or any nearby pages, if it had moved by a page in other printings). Anyone have any idea what might have been meant here?

-Harry

Color?

Mar. 20th, 2007 02:42 pm
sniffnoy: (Chu-Chu Zig)
So I get out the newspaper yesterday, I turn to the comics, and they're... in color? What?

Now I'm quite certain that weekday comics are not *written* in color. So The Record must be adding it themselves. (Why they're wasting their time colorizing black and white comics rather than actually finding better ones is also a pretty obvious question to ask, but not one I'm going to address here.) Now from what little I've seen they look like they're doing a good job of it, but I have to say this makes me distinctly uneasy.

Also, I just noticed that I can't find a credit for whoever added the color.

-Sniffnoy

June 2025

S M T W T F S
1234567
891011121314
15161718192021
2223 2425262728
2930     
Page generated Jul. 25th, 2025 09:58 pm
Powered by Dreamwidth Studios